SU\G(𝔸)/K·U
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Henry H. Kim is a mathematician at the University of Toronto known for his research in automorphic forms, representation theory, and the Langlands program. His work has contributed to the understanding of L-functions and functoriality, key areas in modern number theory. He has published on topics such as the Langlands–Shahidi method and has collaborated with other mathematicians investigating connections between automorphic forms and various branches of number theory.

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Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂

2002-10-30
Henry Kim
In this paper we prove the functoriality of the exterior square of cusp forms on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G upper L 4"> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow … In this paper we prove the functoriality of the exterior square of cusp forms on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G upper L 4"> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">GL_{4}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> as automorphic forms on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G upper L 6"> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>6</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">GL_{6}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and the symmetric fourth of cusp forms on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G upper L 2"> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">GL_{2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> as automorphic forms on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G upper L 5"> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>5</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">GL_{5}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We prove these by applying a converse theorem of Cogdell and Piatetski-Shapiro to analytic properties of certain <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding="application/x-tex">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-functions obtained by the Langlands-Shahidi method. We give several applications: First, we prove the weak Ramanujan property of cuspidal representations of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G upper L 4"> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">GL_{4}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and the absolute convergence of the exterior square <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding="application/x-tex">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-functions of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G upper L 4"> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">GL_{4}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Second, we prove that the fourth symmetric power <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding="application/x-tex">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-functions of cuspidal representations of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G upper L 2"> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">GL_{2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are entire, except for those of dihedral and tetrahedral type. Third, we prove the bound <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="three twenty-sixths"> <mml:semantics> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>26</mml:mn> </mml:mfrac> <mml:annotation encoding="application/x-tex">\frac {3}{26}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for Hecke eigenvalues of Maass forms over any number field.

Towards an Ontology-Driven Blockchain Design for Supply Chain Provenance

2016-01-01
Henry Kim , Marek Laskowski
An interesting research problem in our age of Big Data is that of determining provenance. Granular evaluation of provenance of physical goods -- e.g. tracking ingredients of a pharmaceutical or … An interesting research problem in our age of Big Data is that of determining provenance. Granular evaluation of provenance of physical goods -- e.g. tracking ingredients of a pharmaceutical or demonstrating authenticity of luxury goods -- has often not been possible with today's items that are produced and transported in complex, inter-organizational, often internationally-spanning supply chains. Recent adoption of Internet of Things and Blockchain technologies give promise at better supply chain provenance. We are particularly interested in the blockchain as many favoured use cases of blockchain are for provenance tracking. We are also interested in applying ontologies as there has been some work done on knowledge provenance, traceability, and food provenance using ontologies. In this paper, we make a case for why ontologies can contribute to blockchain design. To support this case, we analyze a traceability ontology and translate some of its representations to smart contracts that execute a provenance trace and enforce traceability constraints on the Ethereum blockchain platform.
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A Case Study for Grain Quality Assurance Tracking based on a Blockchain Business Network

2018-01-01
Percival Lucena , Alécio Pedro Delazari Binotto , Fernanda da Silva Momo +1 more
One of the key processes in Agriculture is quality measurement throughout the transportation of grains along its complex supply chain. This procedure is suitable for failures, such as delays to … One of the key processes in Agriculture is quality measurement throughout the transportation of grains along its complex supply chain. This procedure is suitable for failures, such as delays to final destinations, poor monitoring, and frauds. To address the grain quality measurement challenge through the transportation chain, novel technologies, such as Distributed Ledger and Blockchain, can bring more efficiency and resilience to the process. Particularly, Blockchain is a new type of distributed database in which transactions are securely appended using cryptography and hashed pointers. Those transactions can be generated and ruled by special network-embedded software -- known as smart contracts -- that may be public to all nodes of the network or may be private to a specific set of peer nodes. This paper analyses the implementation of Blockchain technology targeting grain quality assurance tracking in a real scenario. Preliminary results support a potential demand for a Blockchain-based certification that would lead to an added valuation of around 15% for GM-free soy in the scope of a Grain Exporter Business Network in Brazil.

A Perspective on Blockchain Smart Contracts: Reducing Uncertainty and Complexity in Value Exchange

2017-07-01
Henry Kim , Marek Laskowski
The blockchain constitutes a technology-based, rather than social or regulation based, means to lower uncertainty about one another in order to exchange value. However, its use may very well also … The blockchain constitutes a technology-based, rather than social or regulation based, means to lower uncertainty about one another in order to exchange value. However, its use may very well also lead to increased complexity resulting from having to subsume work that displaced intermediary institutions had performed. We present our perspective that smart contracts may be used to mitigate this increased complexity. We further posit that smart contracts can be delineated according to complexity: Smart contracts that can be verified objectively without much uncertainty belong in an inter- organizational context; those that cannot be objectively verified belong in an intra- organizational context. We state that smart contracts that implement a formal (e.g. mathematical or simulation) model are especially beneficial for both contexts: They can be used to express and enforce inter-organizational agreements, and their basis in a common formalism may ensure effective evaluation and comparison between different intra-organizational contracts. Finally, we present a case study of our perspective by describing Intellichain, which implements formal, agent-based simulation model as a smart contract to provide epidemiological decision support.
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Design and Field Implementation of Blockchain Based Renewable Energy Trading in Residential Communities

2019-11-01
Shivam Saxena , Hany E. Z. Farag , Aidan Brookson +2 more
This paper proposes a peer to peer (P2P), blockchain based energy trading market platform for residential communities with the objective of reducing overall community peak demand and household electricity bills. … This paper proposes a peer to peer (P2P), blockchain based energy trading market platform for residential communities with the objective of reducing overall community peak demand and household electricity bills. Smart homes within the community place energy bids for its available distributed energy resources (DERs) for each discrete trading period during a day, and a double auction mechanism is used to clear the market and compute the market clearing price (MCP). The marketplace is implemented on a permissioned blockchain infrastructure, where bids are stored to the immutable ledger and smart contracts are used to implement the MCP calculation and award service contracts to all winning bids. Utilizing the blockchain obviates the need for a trusted, centralized auctioneer, and eliminates vulnerability to a single point of failure. Simulation results show that the platform enables a community peak demand reduction of 46%, as well as a weekly savings of 6%. The platform is also tested at a real-world Canadian microgrid using the Hyperledger Fabric blockchain framework, to show the end to end connectivity of smart home DERs to the platform.
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A Perspective on Blockchain Smart Contracts: Reducing Uncertainty and Complexity in Value Exchange

2017-01-01
Henry Kim , Marek Laskowski
The blockchain constitutes a technology-based, rather than social or regulation based, means to lower uncertainty about one another in order to exchange value. However, its use may very well also … The blockchain constitutes a technology-based, rather than social or regulation based, means to lower uncertainty about one another in order to exchange value. However, its use may very well also lead to increased complexity resulting from having to subsume work that displaced intermediary institutions had performed. We present our perspective that smart contracts may be used to mitigate this increased complexity. We further posit that smart contracts can be delineated according to complexity: Smart contracts that can be verified objectively without much uncertainty belong in an inter-organizational context; those that cannot be objectively verified belong in an intra-organizational context. We state that smart contracts that implement a formal (e.g. mathematical or simulation) model are especially beneficial for both contexts: They can be used to express and enforce inter-organizational agreements, and their basis in a common formalism may ensure effective evaluation and comparison between different intra-organizational contracts. Finally, we present a case study of our perspective by describing Intellichain, which implements formal, agent-based simulation model as a smart contract to provide epidemiological decision support.
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A First Step in the Co-Evolution of Blockchain and Ontologies: Towards Engineering an Ontology of Governance at the Blockchain Protocol Level

2018-01-01
Henry Kim , Marek Laskowski , Ning Nan
At the beginning of 2018, there is a growing belief that blockchain technologies constitute a revolutionary innovation in how we transfer value electronically.In that vein, blockchain may be a suitable … At the beginning of 2018, there is a growing belief that blockchain technologies constitute a revolutionary innovation in how we transfer value electronically.In that vein, blockchain may be a suitable complement to ontologies to achieve a big part of Tim Berners-Lee's vision of the semantic Web.We believe that if this complementarity is to be achieved blockchain and ontologies must co-evolve.In this paper, we focus on what and how to engineer models, methods, designs, and implementations for this co-evolution.As a first step in this co-evolution, we propose a conceptual design of a governance ontology represented as meta-data tags to be embedded and instantiated in a smart contract at the blockchain protocol level.We develop this design by examining and analyzing smart contracts from the infamous The DAO experiment on the Ethereum blockchain.We believe there are two contributions of this paper: it serves to inform and implore the blockchain and ontology communities to recognize and collaborate with each other; and it outlines a roadmap for engineering artifacts to bridge the gap between blockchain community's focus on protocol-level blockchain interoperability and the ontology community's focus on semantic-level interoperability.
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Rapid Prototyping of a Text Mining Application for Cryptocurrency Market Intelligence

2016-07-01
Marek Laskowski , Henry Kim
Blockchain represents a technology for establishing a shared, immutable version of the truth between a network of participants that do not trust one another, and therefore has the potential to … Blockchain represents a technology for establishing a shared, immutable version of the truth between a network of participants that do not trust one another, and therefore has the potential to disrupt any financial or other industries that rely on third-parties to establish trust. In order to better understand the current ecosystem of Blockchain applications, a scalable proof-of-concept pipeline for analysis of multiple streams of semi-structured data posted on social media is demonstrated, based on open source components. Deep Web as well as conventional social media are considered. Preliminary analysis suggests that data found in the Deep Web is complimentary to that available on the conventional web. Future work is described that will scale the system to cloud-based, real-time, analysis of multiple data streams, with Information Extraction (IE) (ex. sentiment analysis) and Machine Learning capability.
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Quantum affine algebras, canonical bases, and<i>q</i>-deformation of arithmetical functions

2012-04-10
Henry Kim , Kyu‐Hwan Lee
We obtain affine analogs of the Gindikin-Karpelevich and Casselman-Shalika formulas as sums over Kashiwara and Lusztig's canonical bases.As suggested by these formulas, we define natural q-deformation of arithmetical functions such … We obtain affine analogs of the Gindikin-Karpelevich and Casselman-Shalika formulas as sums over Kashiwara and Lusztig's canonical bases.As suggested by these formulas, we define natural q-deformation of arithmetical functions such as (multi)partition functions and Ramanujan τ -functions, and prove various identities among them.In some examples we recover classical identities by taking limits.Additionally, we consider q-deformation of the Kostant function and study certain q-polynomials whose special values are weight multiplicities.
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Rapid Prototyping of a Text Mining Application for Cryptocurrency Market Intelligence

2016-01-01
Marek Laskowski , Henry Kim
Blockchain represents a technology for establishing a shared, immutable version of the truth between a network of participants that do not trust one another, and therefore has the potential to … Blockchain represents a technology for establishing a shared, immutable version of the truth between a network of participants that do not trust one another, and therefore has the potential to disrupt any financial or other industries that rely on third-parties to establish trust. Recent trends in computing including: prevalence of Free and Open Source Software (FOSS); easy access to High Performance Computing (HPC i.e. 'The Cloud'); and increasingly advanced analytics capabilities such as Natural Language Processing (NLP) and Machine Learning (ML) allow for rapidly prototyping applications for analysis of trends in the emergence of Blockchain technology. A scaleable proof-of-concept pipeline that lays the groundwork for analysis of multiple streams of semi-structured data posted on social media is demonstrated. Preliminary analysis and performance metrics are presented and discussed. Future work is described that will scale the system to cloud-based, real-time, analysis of multiple data streams, with Information Extraction (IE) (ex. sentiment analysis) and Machine Learning capability.
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Local Langlands correspondence

2009-03-09
James Cogdell , Henry Kim , M. Narasimha Murty
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Towards an Ontology-Driven Blockchain Design for Supply Chain Provenance

2016-08-28
Henry Kim , Marek Laskowski
An interesting research problem in our age of Big Data is that of determining provenance. Granular evaluation of provenance of physical goods--e.g. tracking ingredients of a pharmaceutical or demonstrating authenticity … An interesting research problem in our age of Big Data is that of determining provenance. Granular evaluation of provenance of physical goods--e.g. tracking ingredients of a pharmaceutical or demonstrating authenticity of luxury goods--has often not been possible with today's items that are produced and transported in complex, inter-organizational, often internationally-spanning supply chains. Recent adoption of Internet of Things and Blockchain technologies give promise at better supply chain provenance. We are particularly interested in the blockchain as many favoured use cases of blockchain are for provenance tracking. We are also interested in applying ontologies as there has been some work done on knowledge provenance, traceability, and food provenance using ontologies. In this paper, we make a case for why ontologies can contribute to blockchain design. To support this case, we analyze a traceability ontology and translate some of its representations to smart contracts that execute a provenance trace and enforce traceability constraints on the Ethereum blockchain platform.

Privacy-Preserving Blockchain Mining: Sybil-resistance by Proof-of-Useful-Work

2019-07-20
Hjalmar Turesson , Alexandra Roatiş , Marek Laskowski +1 more
Blockchains rely on a consensus among participants to achieve decentralization and security. However, reaching consensus in an online, digital world where identities are not tied to physical users is a … Blockchains rely on a consensus among participants to achieve decentralization and security. However, reaching consensus in an online, digital world where identities are not tied to physical users is a challenging problem. Proof-of-work (PoW) provides a solution by linking representation to a valuable, physical resource. This has worked well, currently securing Bitcoins $100 B value. However, the Bitcoin network uses a tremendous amount of specialized hardware and energy, and since the utility of these resources is strictly limited to blockchain security, the resources used are not useful other purposes. Here, we propose an alternative consensus scheme that directs the computational resources to a task with utility beyond blockchain security, aiming at better resource utilization. The key idea is to channel the resources to optimization of machine learning (ML) models by setting up decentralized ML competitions. This is achieved by a hybrid consensus scheme relying on three parties: data providers, miners, and a committee. The data provider makes data available and provides payment in return for the best model, miners compete about the payment and access to the committee by producing ML optimized models, and the committee controls the ML competition.

Blockchain Based Transactive Energy Systems for Voltage Regulation

2019-01-01
Shivam Saxena , Hany E. Z. Farag , Hjalmar Turesson +1 more
Transactive Energy Systems (TES) are modern mechanisms in electric power systems that allow disparate control agents to utilize distributed generation units (DGs) to engage in energy transactions and provide ancillary … Transactive Energy Systems (TES) are modern mechanisms in electric power systems that allow disparate control agents to utilize distributed generation units (DGs) to engage in energy transactions and provide ancillary services to the grid. Although voltage regulation is a crucial ancillary service within active distribution networks (ADNs), previous work has not adequately explored how this service can be offered in terms of its incentivization, contract auditability and enforcement. Blockchain technology shows promise in being a key enabler of TES, allowing agents to engage in trustless, persistent transactions that are both enforceable and auditable. To that end, this paper proposes a blockchain based TES that enables agents to receive incentives for providing voltage regulation services by i) maintaining an auditable reputation rating for each agent that is increased proportionately with each mitigation of a voltage violation, ii) utilizing smart contracts to enforce the validity of each transaction and penalize reputation ratings in case of a mitigation failure and iii) automating the negotiation and bidding of agent services by implementing the contract net protocol (CNP) as a smart contract. Experimental results on both simulated and real-world ADNs are executed to demonstrate the efficacy of the proposed system.

Towards an Ontology-Driven Blockchain Design for Supply Chain Provenance

2016-01-01
Henry Kim , Marek Laskowski
An interesting research problem in our age of Big Data is that of determining provenance. Granular evaluation of provenance of physical goods--e.g. tracking ingredients of a pharmaceutical or demonstrating authenticity … An interesting research problem in our age of Big Data is that of determining provenance. Granular evaluation of provenance of physical goods--e.g. tracking ingredients of a pharmaceutical or demonstrating authenticity of luxury goods--has often not been possible with today's items that are produced and transported in complex, inter-organizational, often internationally-spanning supply chains. Recent adoption of Internet of Things and Blockchain technologies give promise at better supply chain provenance. We are particularly interested in the blockchain as many favoured use cases of blockchain are for provenance tracking. We are also interested in applying ontologies as there has been some work done on knowledge provenance, traceability, and food provenance using ontologies. In this paper, we make a case for why ontologies can contribute to blockchain design. To support this case, we analyze a traceability ontology and translate some of its representations to smart contracts that execute a provenance trace and enforce traceability constraints on the Ethereum blockchain platform.
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Weakly holomorphic modular forms and rank two hyperbolic Kac-Moody algebras

2015-03-13
Henry Kim , Kyu‐Hwan Lee , Yichao Zhang
In this paper, we compute basis elements of certain spaces of weight <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="0"> <mml:semantics> <mml:mn>0</mml:mn> <mml:annotation encoding="application/x-tex">0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> weakly holomorphic modular forms and consider … In this paper, we compute basis elements of certain spaces of weight <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="0"> <mml:semantics> <mml:mn>0</mml:mn> <mml:annotation encoding="application/x-tex">0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> weakly holomorphic modular forms and consider the integrality of Fourier coefficients of the modular forms. We use the results to construct automorphic correction of the rank <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2"> <mml:semantics> <mml:mn>2</mml:mn> <mml:annotation encoding="application/x-tex">2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> hyperbolic Kac-Moody algebras <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper H left-parenthesis a right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">H</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>a</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathcal H(a)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="a equals 4 comma 5 comma 6"> <mml:semantics> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> <mml:mo>,</mml:mo> <mml:mn>5</mml:mn> <mml:mo>,</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">a=4,5,6</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, through Hilbert modular forms explicitly given by Borcherds lifts of the weakly holomorphic modular forms. We also compute asymptotics of the Fourier coefficients as they are related to root multiplicities of the rank <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2"> <mml:semantics> <mml:mn>2</mml:mn> <mml:annotation encoding="application/x-tex">2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> hyperbolic Kac-Moody algebras. This work is a continuation of an earlier work of the first and second authors, where automorphic correction was constructed for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper H left-parenthesis a right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">H</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>a</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathcal H(a)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="a equals 3 comma 11 comma 66"> <mml:semantics> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mn>11</mml:mn> <mml:mo>,</mml:mo> <mml:mn>66</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">a=3, 11, 66</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.
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A conditional construction of Artin representations for real analytic Siegel cusp forms of weight (2,1)

2016-01-01
Henry Kim , Takuya Yamauchi

A Perspective on Blockchain Smart Contracts: Reducing Uncertainty and Complexity in Value Exchange

2018-01-01
Henry Kim , Marek Laskowski
The blockchain constitutes a technology-based, rather than social or regulation based, means to lower uncertainty about one another in order to exchange value. However, its use may very well also … The blockchain constitutes a technology-based, rather than social or regulation based, means to lower uncertainty about one another in order to exchange value. However, its use may very well also lead to increased complexity resulting from having to subsume work that displaced intermediary institutions had performed. We present our perspective that smart contracts may be used to mitigate this increased complexity. We further posit that smart contracts can be delineated according to complexity: Smart contracts that can be verified objectively without much uncertainty belong in an inter-organizational context; those that cannot be objectively verified belong in an intra-organizational context. We state that smart contracts that implement a formal (e.g. mathematical or simulation) model are especially beneficial for both contexts: They can be used to express and enforce inter-organizational agreements, and their basis in a common formalism may ensure effective evaluation and comparison between different intra-organizational contracts. Finally, we present a case study of our perspective by describing Intellichain, which implements formal, agent-based simulation model as a smart contract to provide epidemiological decision support.
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Workflow Management on the Blockchain --- Implications and Recommendations

2019-01-01
Jöerg Evermann , Henry Kim
Blockchain technology, originally popularized by cryptocurrencies, has been proposed as an infrastructure technology with applications in many areas of business management. Blockchains provide an immutable record of transactions, which makes … Blockchain technology, originally popularized by cryptocurrencies, has been proposed as an infrastructure technology with applications in many areas of business management. Blockchains provide an immutable record of transactions, which makes them useful in situations where business actors may not fully trust each other. The distributed nature of blockchains makes them particularly suitable for inter-organizational e-Business applications. In this paper we examine the use of blockchains for executing inter-organizational workflows. We discuss architectural options and describe prototype implementations of blockchain-based workflow management systems (WfMS), highlighting differences to traditional WfMS. Our main contribution is the identification of potential problems raised by blockchain infrastructure and recommendations to address them.

Blockchain Based Grid Operation Services for Transactive Energy Systems.

2019-07-19
Shivam Saxena , Hany E. Z. Farag , Hjalmar Turesson +1 more
Transactive Energy Systems (TES) are modern electric power systems that enable decentralized owners of power generation assets to engage in energy transactions and provide computing services that improve the performance … Transactive Energy Systems (TES) are modern electric power systems that enable decentralized owners of power generation assets to engage in energy transactions and provide computing services that improve the performance of power system operation. Blockchain technology is a key enabler of TES, allowing peers to engage in trustless, persistent transactions that are both enforceable and auditable. However, previous work within this context has not adequately explored fraudulent service transactions amongst peers, and its potential negative impact on power system operation. To that end, this paper proposes a blockchain based TES that enables distributed peers (known as agents), to receive incentives for providing grid operation services in the form of voltage regulation, which is a critical operational service. The proposed system i) maintains a trustless reputation rating for each agent that is increased proportionately with each transaction that improves grid operation, ii) utilizes smart contracts to enforce the validity of each transaction and penalizes reputation ratings in case of a fraudulent transaction, iii) automates the negotiation and bidding of agent services by implementing the contract net protocol (CNP) as a smart contract. Experimental results on both simulated and real-world power systems are executed to demonstrate the efficacy of the proposed system.

Workflow Management on BFT Blockchains

2019-01-01
Jöerg Evermann , Henry Kim
Blockchain technology has been proposed as a new infrastructure technology for a wide variety of novel applications. Blockchains provide an immutable record of transactions, making them useful when business actors … Blockchain technology has been proposed as a new infrastructure technology for a wide variety of novel applications. Blockchains provide an immutable record of transactions, making them useful when business actors do not trust each other. Their distributed nature makes them suitable for inter-organizational applications. However, proof-of-work based blockchains are computationally inefficient and do not provide final consensus, although they scale well to large networks. In contrast, blockchains built around Byzantine Fault Tolerance (BFT) algorithms are more efficient and provide immediate and final consensus, but do not scale well to large networks. We argue that this makes them well-suited for workflow management applications that typically include no more than a few dozen participants but require final consensus. In this paper, we discuss architectural options and present a prototype implementation of a BFT-blockchain-based workflow management system (WfMS).

Proof-of-Useful-Work as Dual-Purpose Mechanism for Blockchain and AI: Blockchain Consensus that Enables Privacy Preserving Data Mining

2019-01-01
Hjalmar Turesson , Henry Kim , Marek Laskowski +1 more
Blockchains rely on a consensus among participants to achieve decentralization and security. However, reaching consensus in an online, digital world where identities are not tied to physical users is a … Blockchains rely on a consensus among participants to achieve decentralization and security. However, reaching consensus in an online, digital world where identities are not tied to physical users is a challenging problem. Proof-of-work provides a solution by linking representation to a valuable, physical resource. While this has worked well, it uses a tremendous amount of specialized hardware and energy, with no utility beyond blockchain security. Here, we propose an alternative consensus scheme that directs the computational resources to the optimization of machine learning (ML) models, a task with more general utility. This is achieved by a hybrid consensus scheme relying on three parties: data providers, miners, and a committee. The data provider makes data available and provides payment in return for the best model, miners compete about the payment and access to the committee by producing ML optimized models, and the committee controls the ML competition.

Lectures on Automorphic 𝐿-functions

2009-03-09
James Cogdell , Henry Kim , M. Murty

A First Step in the Co-Evolution of Blockchain and Ontologies: Towards Engineering an Ontology of Governance at the Blockchain Protocol Level

2018-01-01
Henry Kim , Marek Laskowski , Ning Nan
At the beginning of 2018, there is a growing belief that blockchain technologies constitute a revolutionary innovation in how we transfer value electronically. In that vein, blockchain may be a … At the beginning of 2018, there is a growing belief that blockchain technologies constitute a revolutionary innovation in how we transfer value electronically. In that vein, blockchain may be a suitable complement to ontologies to achieve a big part of the vision of the semantic Web by Tim Berners-Lee. We believe that if this complementarity is to be achieved blockchain and ontologies must co-evolve. In this paper, we focus on what and how to engineer models, methods, designs, and implementations for this co-evolution. As a first step in this co-evolution, we propose a conceptual design of a governance ontology represented as meta-data tags to be embedded and instantiated in a smart contract at the blockchain protocol level. We develop this design by examining and analyzing smart contracts from the infamous The DAO experiment on the Ethereum blockchain. We believe there are two contributions of this paper: it serves to inform and implore the blockchain and ontology communities to recognize and collaborate with each other; and it outlines a roadmap for engineering artifacts to bridge the gap between blockchain community focus on protocol-level blockchain interoperability and the ontology community focus on semantic-level interoperability.
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Token Economics in Real-Life: Cryptocurrency and Incentives Design for Insolar Blockchain Network

2019-01-01
Henry Kim , Marek Laskowski , Michael Zargham +3 more
The study of how to set up cryptocurrency incentive mechanisms and to operationalize governance is token economics. Given the $250 billion market cap for cryptocurrencies, there is compelling need to … The study of how to set up cryptocurrency incentive mechanisms and to operationalize governance is token economics. Given the $250 billion market cap for cryptocurrencies, there is compelling need to investigate this topic. In this paper, we present facets of the token engineering process for a real-life 80-person Swiss blockchain startup, Insolar. We show how Insolar used systems modeling and simulation combined with cryptocurrency expertise to design a mechanism to incentivize enterprises and individual users to use their new MainNet public blockchain network. The study showed subsidy pools that incentivize application developers to develop on the network does indeed have the desired positive effect on MainNet adoption. For a startup like Insolar whose success hinge upon how well their model incentivizes various stakeholders to participate on their MainNet network versus that of numerous alternatives, this token economics simulation analysis provides invaluable insights.

The smallest prime in a conjugacy class and the first sign change for automorphic 𝐿-functions

2020-08-19
Peter J. Cho , Henry Kim
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding="application/x-tex">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be an <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S Subscript n"> <mml:semantics> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:annotation … Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding="application/x-tex">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be an <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S Subscript n"> <mml:semantics> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">S_n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-field. For a nonidentity conjugacy class <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C"> <mml:semantics> <mml:mi>C</mml:mi> <mml:annotation encoding="application/x-tex">C</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, define <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N Subscript upper K comma upper C"> <mml:semantics> <mml:msub> <mml:mi>N</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>K</mml:mi> <mml:mo>,</mml:mo> <mml:mi>C</mml:mi> </mml:mrow> </mml:msub> <mml:annotation encoding="application/x-tex">N_{K,C}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> to be the smallest prime <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that Frob<inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="Subscript p Baseline element-of upper C"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi/> <mml:mi>p</mml:mi> </mml:msub> <mml:mo>∈</mml:mo> <mml:mi>C</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">_p\in C</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. By using the observation that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N Subscript upper K comma upper C"> <mml:semantics> <mml:msub> <mml:mi>N</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>K</mml:mi> <mml:mo>,</mml:mo> <mml:mi>C</mml:mi> </mml:mrow> </mml:msub> <mml:annotation encoding="application/x-tex">N_{K,C}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is interpreted as the first prime sign change of the Dirichlet coefficients of automorphic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding="application/x-tex">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-functions, we improve the known bound on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N Subscript upper K comma upper C"> <mml:semantics> <mml:msub> <mml:mi>N</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>K</mml:mi> <mml:mo>,</mml:mo> <mml:mi>C</mml:mi> </mml:mrow> </mml:msub> <mml:annotation encoding="application/x-tex">N_{K,C}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n equals 3 comma 4 comma 5"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mn>4</mml:mn> <mml:mo>,</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">n=3,4,5</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. (For <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n equals 5"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">n=5</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we need to assume the strong Artin conjecture.)

Data Analytics using Ontologies of Management Theories: Towards Implementing 'From Theory to Practice'

2016-08-28
Henry Kim , Jackie Ho Nam Cheung , Marek Laskowski +1 more
We explore how computational ontologies can be impactful vis-a-vis the developing discipline of science. We posit an approach wherein management theories are represented as formal axioms, and then applied to … We explore how computational ontologies can be impactful vis-a-vis the developing discipline of science. We posit an approach wherein management theories are represented as formal axioms, and then applied to draw inferences about data that reside in corporate databases. That is, management theories would be implemented as rules within a data analytics engine. We demonstrate a case study development of such an ontology by formally representing an accounting theory in First-Order Logic. Though quite preliminary, the idea that an information technology, namely ontologies, can potentially actualize the academic cliche, From Theory to Practice, and be applicable to the burgeoning domain of data analytics is novel and exciting.

Local 𝐿-functions and functional equations

2009-03-09
James Cogdell , Henry Kim , M. Narasimha Murty

Eulerian integral representations

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

The Kim-Sarnak theorem

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Generic representations and their Whittaker models

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Local 𝐿-functions: The non-Archimedean case

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

The Langlands-Tunnell theorem

2009-03-09
James Cogdell , Henry Kim , M. Narasimha Murty

Eisenstein series and constant terms

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Modular forms and their 𝐿-functions

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

𝐿-groups and automorphic 𝐿-functions

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Oscillations of Fourier coefficients of cusp forms

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Functoriality of the symmetric fourth

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Zeros and poles of Artin 𝐿-functions

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Introduction to Artin 𝐿-functions

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Langlands functoriality conjecture

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty
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Holomorphy and bounded in vertical strips

2009-03-09
James Cogdell , Henry Kim , M. Narasimha Murty
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Functoriality of the symmetric cube

2009-03-09
James Cogdell , Henry Kim , M. Murty

Meromorphic continuation of 𝐿-functions

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty
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Kloosterman sums and Selberg’s conjecture

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Converse theorem of Cogdell and Piatetski-Shapiro

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

The Sato-Tate conjecture

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Fourier expansions and multiplicity one theorems

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Local coefficients and non-constant terms

2009-03-09
James Cogdell , Henry Kim , M. Narasimha Murty

Refined estimates for Fourier coefficients of cusp forms

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Propensity matched analysis of single access technique for Impella-assisted unprotected left main percutaneous coronary intervention

2025-05-01
Raef Fadel , Benjamin C. Hofeld , Herbert D. Aronow +7 more

𝑝-adic limit of the Eisenstein series on the exceptional group of type 𝐸_{7,3}

2024-03-29
Hidenori Katsurada , Henry Kim
In this paper, we show that the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic limit of a family of Eisenstein series on the exceptional domain … In this paper, we show that the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic limit of a family of Eisenstein series on the exceptional domain where the exceptional group of type <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E Subscript 7 comma 3"> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>7</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> <mml:annotation encoding="application/x-tex">E_{7,3}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> acts is an ordinary modular form for a congruence subgroup.

The smallest prime in a conjugacy class and the first sign change for automorphic 𝐿-functions

2020-08-19
Peter J. Cho , Henry Kim
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding="application/x-tex">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be an <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S Subscript n"> <mml:semantics> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:annotation … Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding="application/x-tex">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be an <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S Subscript n"> <mml:semantics> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">S_n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-field. For a nonidentity conjugacy class <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C"> <mml:semantics> <mml:mi>C</mml:mi> <mml:annotation encoding="application/x-tex">C</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, define <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N Subscript upper K comma upper C"> <mml:semantics> <mml:msub> <mml:mi>N</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>K</mml:mi> <mml:mo>,</mml:mo> <mml:mi>C</mml:mi> </mml:mrow> </mml:msub> <mml:annotation encoding="application/x-tex">N_{K,C}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> to be the smallest prime <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that Frob<inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="Subscript p Baseline element-of upper C"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi/> <mml:mi>p</mml:mi> </mml:msub> <mml:mo>∈</mml:mo> <mml:mi>C</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">_p\in C</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. By using the observation that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N Subscript upper K comma upper C"> <mml:semantics> <mml:msub> <mml:mi>N</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>K</mml:mi> <mml:mo>,</mml:mo> <mml:mi>C</mml:mi> </mml:mrow> </mml:msub> <mml:annotation encoding="application/x-tex">N_{K,C}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is interpreted as the first prime sign change of the Dirichlet coefficients of automorphic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding="application/x-tex">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-functions, we improve the known bound on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N Subscript upper K comma upper C"> <mml:semantics> <mml:msub> <mml:mi>N</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>K</mml:mi> <mml:mo>,</mml:mo> <mml:mi>C</mml:mi> </mml:mrow> </mml:msub> <mml:annotation encoding="application/x-tex">N_{K,C}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n equals 3 comma 4 comma 5"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mn>4</mml:mn> <mml:mo>,</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">n=3,4,5</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. (For <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n equals 5"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">n=5</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we need to assume the strong Artin conjecture.)

Design and Field Implementation of Blockchain Based Renewable Energy Trading in Residential Communities

2019-11-01
Shivam Saxena , Hany E. Z. Farag , Aidan Brookson +2 more
This paper proposes a peer to peer (P2P), blockchain based energy trading market platform for residential communities with the objective of reducing overall community peak demand and household electricity bills. … This paper proposes a peer to peer (P2P), blockchain based energy trading market platform for residential communities with the objective of reducing overall community peak demand and household electricity bills. Smart homes within the community place energy bids for its available distributed energy resources (DERs) for each discrete trading period during a day, and a double auction mechanism is used to clear the market and compute the market clearing price (MCP). The marketplace is implemented on a permissioned blockchain infrastructure, where bids are stored to the immutable ledger and smart contracts are used to implement the MCP calculation and award service contracts to all winning bids. Utilizing the blockchain obviates the need for a trusted, centralized auctioneer, and eliminates vulnerability to a single point of failure. Simulation results show that the platform enables a community peak demand reduction of 46%, as well as a weekly savings of 6%. The platform is also tested at a real-world Canadian microgrid using the Hyperledger Fabric blockchain framework, to show the end to end connectivity of smart home DERs to the platform.
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Privacy-Preserving Blockchain Mining: Sybil-resistance by Proof-of-Useful-Work

2019-07-20
Hjalmar Turesson , Alexandra Roatiş , Marek Laskowski +1 more
Blockchains rely on a consensus among participants to achieve decentralization and security. However, reaching consensus in an online, digital world where identities are not tied to physical users is a … Blockchains rely on a consensus among participants to achieve decentralization and security. However, reaching consensus in an online, digital world where identities are not tied to physical users is a challenging problem. Proof-of-work (PoW) provides a solution by linking representation to a valuable, physical resource. This has worked well, currently securing Bitcoins $100 B value. However, the Bitcoin network uses a tremendous amount of specialized hardware and energy, and since the utility of these resources is strictly limited to blockchain security, the resources used are not useful other purposes. Here, we propose an alternative consensus scheme that directs the computational resources to a task with utility beyond blockchain security, aiming at better resource utilization. The key idea is to channel the resources to optimization of machine learning (ML) models by setting up decentralized ML competitions. This is achieved by a hybrid consensus scheme relying on three parties: data providers, miners, and a committee. The data provider makes data available and provides payment in return for the best model, miners compete about the payment and access to the committee by producing ML optimized models, and the committee controls the ML competition.

Design and Field Implementation of Blockchain Based Renewable Energy Trading in Residential Communities

2019-07-20
Shivam Saxena , Hany E. Z. Farag , Aidan Brookson +2 more
This paper proposes a peer to peer (P2P), blockchain based energy trading market platform for residential communities with the objective of reducing overall community peak demand and household electricity bills. … This paper proposes a peer to peer (P2P), blockchain based energy trading market platform for residential communities with the objective of reducing overall community peak demand and household electricity bills. Smart homes within the community place energy bids for its available distributed energy resources (DERs) for each discrete trading period during a day, and a double auction mechanism is used to clear the market and compute the market clearing price (MCP). The marketplace is implemented on a permissioned blockchain infrastructure, where bids are stored to the immutable ledger and smart contracts are used to implement the MCP calculation and award service contracts to all winning bids. Utilizing the blockchain obviates the need for a trusted, centralized auctioneer, and eliminates vulnerability to a single point of failure. Simulation results show that the platform enables a community peak demand reduction of 46%, as well as a weekly savings of 6%. The platform is also tested at a real-world Canadian microgrid using the Hyperledger Fabric blockchain framework, to show the end to end connectivity of smart home DERs to the platform.

Blockchain Based Grid Operation Services for Transactive Energy Systems.

2019-07-19
Shivam Saxena , Hany E. Z. Farag , Hjalmar Turesson +1 more
Transactive Energy Systems (TES) are modern electric power systems that enable decentralized owners of power generation assets to engage in energy transactions and provide computing services that improve the performance … Transactive Energy Systems (TES) are modern electric power systems that enable decentralized owners of power generation assets to engage in energy transactions and provide computing services that improve the performance of power system operation. Blockchain technology is a key enabler of TES, allowing peers to engage in trustless, persistent transactions that are both enforceable and auditable. However, previous work within this context has not adequately explored fraudulent service transactions amongst peers, and its potential negative impact on power system operation. To that end, this paper proposes a blockchain based TES that enables distributed peers (known as agents), to receive incentives for providing grid operation services in the form of voltage regulation, which is a critical operational service. The proposed system i) maintains a trustless reputation rating for each agent that is increased proportionately with each transaction that improves grid operation, ii) utilizes smart contracts to enforce the validity of each transaction and penalizes reputation ratings in case of a fraudulent transaction, iii) automates the negotiation and bidding of agent services by implementing the contract net protocol (CNP) as a smart contract. Experimental results on both simulated and real-world power systems are executed to demonstrate the efficacy of the proposed system.

Workflow Management on the Blockchain --- Implications and Recommendations

2019-01-01
Jöerg Evermann , Henry Kim
Blockchain technology, originally popularized by cryptocurrencies, has been proposed as an infrastructure technology with applications in many areas of business management. Blockchains provide an immutable record of transactions, which makes … Blockchain technology, originally popularized by cryptocurrencies, has been proposed as an infrastructure technology with applications in many areas of business management. Blockchains provide an immutable record of transactions, which makes them useful in situations where business actors may not fully trust each other. The distributed nature of blockchains makes them particularly suitable for inter-organizational e-Business applications. In this paper we examine the use of blockchains for executing inter-organizational workflows. We discuss architectural options and describe prototype implementations of blockchain-based workflow management systems (WfMS), highlighting differences to traditional WfMS. Our main contribution is the identification of potential problems raised by blockchain infrastructure and recommendations to address them.

Workflow Management on BFT Blockchains

2019-01-01
Jöerg Evermann , Henry Kim
Blockchain technology has been proposed as a new infrastructure technology for a wide variety of novel applications. Blockchains provide an immutable record of transactions, making them useful when business actors … Blockchain technology has been proposed as a new infrastructure technology for a wide variety of novel applications. Blockchains provide an immutable record of transactions, making them useful when business actors do not trust each other. Their distributed nature makes them suitable for inter-organizational applications. However, proof-of-work based blockchains are computationally inefficient and do not provide final consensus, although they scale well to large networks. In contrast, blockchains built around Byzantine Fault Tolerance (BFT) algorithms are more efficient and provide immediate and final consensus, but do not scale well to large networks. We argue that this makes them well-suited for workflow management applications that typically include no more than a few dozen participants but require final consensus. In this paper, we discuss architectural options and present a prototype implementation of a BFT-blockchain-based workflow management system (WfMS).

Token Economics in Real-Life: Cryptocurrency and Incentives Design for Insolar Blockchain Network

2019-01-01
Henry Kim , Marek Laskowski , Michael Zargham +3 more
The study of how to set up cryptocurrency incentive mechanisms and to operationalize governance is token economics. Given the $250 billion market cap for cryptocurrencies, there is compelling need to … The study of how to set up cryptocurrency incentive mechanisms and to operationalize governance is token economics. Given the $250 billion market cap for cryptocurrencies, there is compelling need to investigate this topic. In this paper, we present facets of the token engineering process for a real-life 80-person Swiss blockchain startup, Insolar. We show how Insolar used systems modeling and simulation combined with cryptocurrency expertise to design a mechanism to incentivize enterprises and individual users to use their new MainNet public blockchain network. The study showed subsidy pools that incentivize application developers to develop on the network does indeed have the desired positive effect on MainNet adoption. For a startup like Insolar whose success hinge upon how well their model incentivizes various stakeholders to participate on their MainNet network versus that of numerous alternatives, this token economics simulation analysis provides invaluable insights.

Blockchain Based Transactive Energy Systems for Voltage Regulation

2019-01-01
Shivam Saxena , Hany E. Z. Farag , Hjalmar Turesson +1 more
Transactive Energy Systems (TES) are modern mechanisms in electric power systems that allow disparate control agents to utilize distributed generation units (DGs) to engage in energy transactions and provide ancillary … Transactive Energy Systems (TES) are modern mechanisms in electric power systems that allow disparate control agents to utilize distributed generation units (DGs) to engage in energy transactions and provide ancillary services to the grid. Although voltage regulation is a crucial ancillary service within active distribution networks (ADNs), previous work has not adequately explored how this service can be offered in terms of its incentivization, contract auditability and enforcement. Blockchain technology shows promise in being a key enabler of TES, allowing agents to engage in trustless, persistent transactions that are both enforceable and auditable. To that end, this paper proposes a blockchain based TES that enables agents to receive incentives for providing voltage regulation services by i) maintaining an auditable reputation rating for each agent that is increased proportionately with each mitigation of a voltage violation, ii) utilizing smart contracts to enforce the validity of each transaction and penalize reputation ratings in case of a mitigation failure and iii) automating the negotiation and bidding of agent services by implementing the contract net protocol (CNP) as a smart contract. Experimental results on both simulated and real-world ADNs are executed to demonstrate the efficacy of the proposed system.

Proof-of-Useful-Work as Dual-Purpose Mechanism for Blockchain and AI: Blockchain Consensus that Enables Privacy Preserving Data Mining

2019-01-01
Hjalmar Turesson , Henry Kim , Marek Laskowski +1 more
Blockchains rely on a consensus among participants to achieve decentralization and security. However, reaching consensus in an online, digital world where identities are not tied to physical users is a … Blockchains rely on a consensus among participants to achieve decentralization and security. However, reaching consensus in an online, digital world where identities are not tied to physical users is a challenging problem. Proof-of-work provides a solution by linking representation to a valuable, physical resource. While this has worked well, it uses a tremendous amount of specialized hardware and energy, with no utility beyond blockchain security. Here, we propose an alternative consensus scheme that directs the computational resources to the optimization of machine learning (ML) models, a task with more general utility. This is achieved by a hybrid consensus scheme relying on three parties: data providers, miners, and a committee. The data provider makes data available and provides payment in return for the best model, miners compete about the payment and access to the committee by producing ML optimized models, and the committee controls the ML competition.

Design and Field Implementation of Blockchain Based Renewable Energy Trading in Residential Communities

2019-01-01
Shivam Saxena , Hany E. Z. Farag , Aidan Brookson +2 more
This paper proposes a peer to peer (P2P), blockchain based energy trading market platform for residential communities with the objective of reducing overall community peak demand and household electricity bills. … This paper proposes a peer to peer (P2P), blockchain based energy trading market platform for residential communities with the objective of reducing overall community peak demand and household electricity bills. Smart homes within the community place energy bids for its available distributed energy resources (DERs) for each discrete trading period during a day, and a double auction mechanism is used to clear the market and compute the market clearing price (MCP). The marketplace is implemented on a permissioned blockchain infrastructure, where bids are stored to the immutable ledger and smart contracts are used to implement the MCP calculation and award service contracts to all winning bids. Utilizing the blockchain obviates the need for a trusted, centralized auctioneer, and eliminates vulnerability to a single point of failure. Simulation results show that the platform enables a community peak demand reduction of 46%, as well as a weekly savings of 6%. The platform is also tested at a real-world Canadian microgrid using the Hyperledger Fabric blockchain framework, to show the end to end connectivity of smart home DERs to the platform.
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A Perspective on Blockchain Smart Contracts: Reducing Uncertainty and Complexity in Value Exchange

2018-01-01
Henry Kim , Marek Laskowski
The blockchain constitutes a technology-based, rather than social or regulation based, means to lower uncertainty about one another in order to exchange value. However, its use may very well also … The blockchain constitutes a technology-based, rather than social or regulation based, means to lower uncertainty about one another in order to exchange value. However, its use may very well also lead to increased complexity resulting from having to subsume work that displaced intermediary institutions had performed. We present our perspective that smart contracts may be used to mitigate this increased complexity. We further posit that smart contracts can be delineated according to complexity: Smart contracts that can be verified objectively without much uncertainty belong in an inter-organizational context; those that cannot be objectively verified belong in an intra-organizational context. We state that smart contracts that implement a formal (e.g. mathematical or simulation) model are especially beneficial for both contexts: They can be used to express and enforce inter-organizational agreements, and their basis in a common formalism may ensure effective evaluation and comparison between different intra-organizational contracts. Finally, we present a case study of our perspective by describing Intellichain, which implements formal, agent-based simulation model as a smart contract to provide epidemiological decision support.
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A First Step in the Co-Evolution of Blockchain and Ontologies: Towards Engineering an Ontology of Governance at the Blockchain Protocol Level

2018-01-01
Henry Kim , Marek Laskowski , Ning Nan
At the beginning of 2018, there is a growing belief that blockchain technologies constitute a revolutionary innovation in how we transfer value electronically. In that vein, blockchain may be a … At the beginning of 2018, there is a growing belief that blockchain technologies constitute a revolutionary innovation in how we transfer value electronically. In that vein, blockchain may be a suitable complement to ontologies to achieve a big part of the vision of the semantic Web by Tim Berners-Lee. We believe that if this complementarity is to be achieved blockchain and ontologies must co-evolve. In this paper, we focus on what and how to engineer models, methods, designs, and implementations for this co-evolution. As a first step in this co-evolution, we propose a conceptual design of a governance ontology represented as meta-data tags to be embedded and instantiated in a smart contract at the blockchain protocol level. We develop this design by examining and analyzing smart contracts from the infamous The DAO experiment on the Ethereum blockchain. We believe there are two contributions of this paper: it serves to inform and implore the blockchain and ontology communities to recognize and collaborate with each other; and it outlines a roadmap for engineering artifacts to bridge the gap between blockchain community focus on protocol-level blockchain interoperability and the ontology community focus on semantic-level interoperability.
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A Case Study for Grain Quality Assurance Tracking based on a Blockchain Business Network

2018-01-01
Percival Lucena , Alécio Pedro Delazari Binotto , Fernanda da Silva Momo +1 more
One of the key processes in Agriculture is quality measurement throughout the transportation of grains along its complex supply chain. This procedure is suitable for failures, such as delays to … One of the key processes in Agriculture is quality measurement throughout the transportation of grains along its complex supply chain. This procedure is suitable for failures, such as delays to final destinations, poor monitoring, and frauds. To address the grain quality measurement challenge through the transportation chain, novel technologies, such as Distributed Ledger and Blockchain, can bring more efficiency and resilience to the process. Particularly, Blockchain is a new type of distributed database in which transactions are securely appended using cryptography and hashed pointers. Those transactions can be generated and ruled by special network-embedded software -- known as smart contracts -- that may be public to all nodes of the network or may be private to a specific set of peer nodes. This paper analyses the implementation of Blockchain technology targeting grain quality assurance tracking in a real scenario. Preliminary results support a potential demand for a Blockchain-based certification that would lead to an added valuation of around 15% for GM-free soy in the scope of a Grain Exporter Business Network in Brazil.

A First Step in the Co-Evolution of Blockchain and Ontologies: Towards Engineering an Ontology of Governance at the Blockchain Protocol Level

2018-01-01
Henry Kim , Marek Laskowski , Ning Nan
At the beginning of 2018, there is a growing belief that blockchain technologies constitute a revolutionary innovation in how we transfer value electronically.In that vein, blockchain may be a suitable … At the beginning of 2018, there is a growing belief that blockchain technologies constitute a revolutionary innovation in how we transfer value electronically.In that vein, blockchain may be a suitable complement to ontologies to achieve a big part of Tim Berners-Lee's vision of the semantic Web.We believe that if this complementarity is to be achieved blockchain and ontologies must co-evolve.In this paper, we focus on what and how to engineer models, methods, designs, and implementations for this co-evolution.As a first step in this co-evolution, we propose a conceptual design of a governance ontology represented as meta-data tags to be embedded and instantiated in a smart contract at the blockchain protocol level.We develop this design by examining and analyzing smart contracts from the infamous The DAO experiment on the Ethereum blockchain.We believe there are two contributions of this paper: it serves to inform and implore the blockchain and ontology communities to recognize and collaborate with each other; and it outlines a roadmap for engineering artifacts to bridge the gap between blockchain community's focus on protocol-level blockchain interoperability and the ontology community's focus on semantic-level interoperability.
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A Perspective on Blockchain Smart Contracts: Reducing Uncertainty and Complexity in Value Exchange

2017-07-01
Henry Kim , Marek Laskowski
The blockchain constitutes a technology-based, rather than social or regulation based, means to lower uncertainty about one another in order to exchange value. However, its use may very well also … The blockchain constitutes a technology-based, rather than social or regulation based, means to lower uncertainty about one another in order to exchange value. However, its use may very well also lead to increased complexity resulting from having to subsume work that displaced intermediary institutions had performed. We present our perspective that smart contracts may be used to mitigate this increased complexity. We further posit that smart contracts can be delineated according to complexity: Smart contracts that can be verified objectively without much uncertainty belong in an inter- organizational context; those that cannot be objectively verified belong in an intra- organizational context. We state that smart contracts that implement a formal (e.g. mathematical or simulation) model are especially beneficial for both contexts: They can be used to express and enforce inter-organizational agreements, and their basis in a common formalism may ensure effective evaluation and comparison between different intra-organizational contracts. Finally, we present a case study of our perspective by describing Intellichain, which implements formal, agent-based simulation model as a smart contract to provide epidemiological decision support.
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A Perspective on Blockchain Smart Contracts: Reducing Uncertainty and Complexity in Value Exchange

2017-01-01
Henry Kim , Marek Laskowski
The blockchain constitutes a technology-based, rather than social or regulation based, means to lower uncertainty about one another in order to exchange value. However, its use may very well also … The blockchain constitutes a technology-based, rather than social or regulation based, means to lower uncertainty about one another in order to exchange value. However, its use may very well also lead to increased complexity resulting from having to subsume work that displaced intermediary institutions had performed. We present our perspective that smart contracts may be used to mitigate this increased complexity. We further posit that smart contracts can be delineated according to complexity: Smart contracts that can be verified objectively without much uncertainty belong in an inter-organizational context; those that cannot be objectively verified belong in an intra-organizational context. We state that smart contracts that implement a formal (e.g. mathematical or simulation) model are especially beneficial for both contexts: They can be used to express and enforce inter-organizational agreements, and their basis in a common formalism may ensure effective evaluation and comparison between different intra-organizational contracts. Finally, we present a case study of our perspective by describing Intellichain, which implements formal, agent-based simulation model as a smart contract to provide epidemiological decision support.
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Data Analytics using Ontologies of Management Theories: Towards Implementing 'From Theory to Practice'

2016-08-28
Henry Kim , Jackie Ho Nam Cheung , Marek Laskowski +1 more
We explore how computational ontologies can be impactful vis-a-vis the developing discipline of science. We posit an approach wherein management theories are represented as formal axioms, and then applied to … We explore how computational ontologies can be impactful vis-a-vis the developing discipline of science. We posit an approach wherein management theories are represented as formal axioms, and then applied to draw inferences about data that reside in corporate databases. That is, management theories would be implemented as rules within a data analytics engine. We demonstrate a case study development of such an ontology by formally representing an accounting theory in First-Order Logic. Though quite preliminary, the idea that an information technology, namely ontologies, can potentially actualize the academic cliche, From Theory to Practice, and be applicable to the burgeoning domain of data analytics is novel and exciting.

Towards an Ontology-Driven Blockchain Design for Supply Chain Provenance

2016-08-28
Henry Kim , Marek Laskowski
An interesting research problem in our age of Big Data is that of determining provenance. Granular evaluation of provenance of physical goods--e.g. tracking ingredients of a pharmaceutical or demonstrating authenticity … An interesting research problem in our age of Big Data is that of determining provenance. Granular evaluation of provenance of physical goods--e.g. tracking ingredients of a pharmaceutical or demonstrating authenticity of luxury goods--has often not been possible with today's items that are produced and transported in complex, inter-organizational, often internationally-spanning supply chains. Recent adoption of Internet of Things and Blockchain technologies give promise at better supply chain provenance. We are particularly interested in the blockchain as many favoured use cases of blockchain are for provenance tracking. We are also interested in applying ontologies as there has been some work done on knowledge provenance, traceability, and food provenance using ontologies. In this paper, we make a case for why ontologies can contribute to blockchain design. To support this case, we analyze a traceability ontology and translate some of its representations to smart contracts that execute a provenance trace and enforce traceability constraints on the Ethereum blockchain platform.

Rapid Prototyping of a Text Mining Application for Cryptocurrency Market Intelligence

2016-07-01
Marek Laskowski , Henry Kim
Blockchain represents a technology for establishing a shared, immutable version of the truth between a network of participants that do not trust one another, and therefore has the potential to … Blockchain represents a technology for establishing a shared, immutable version of the truth between a network of participants that do not trust one another, and therefore has the potential to disrupt any financial or other industries that rely on third-parties to establish trust. In order to better understand the current ecosystem of Blockchain applications, a scalable proof-of-concept pipeline for analysis of multiple streams of semi-structured data posted on social media is demonstrated, based on open source components. Deep Web as well as conventional social media are considered. Preliminary analysis suggests that data found in the Deep Web is complimentary to that available on the conventional web. Future work is described that will scale the system to cloud-based, real-time, analysis of multiple data streams, with Information Extraction (IE) (ex. sentiment analysis) and Machine Learning capability.
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Rapid Prototyping of a Text Mining Application for Cryptocurrency Market Intelligence

2016-01-01
Marek Laskowski , Henry Kim
Blockchain represents a technology for establishing a shared, immutable version of the truth between a network of participants that do not trust one another, and therefore has the potential to … Blockchain represents a technology for establishing a shared, immutable version of the truth between a network of participants that do not trust one another, and therefore has the potential to disrupt any financial or other industries that rely on third-parties to establish trust. Recent trends in computing including: prevalence of Free and Open Source Software (FOSS); easy access to High Performance Computing (HPC i.e. 'The Cloud'); and increasingly advanced analytics capabilities such as Natural Language Processing (NLP) and Machine Learning (ML) allow for rapidly prototyping applications for analysis of trends in the emergence of Blockchain technology. A scaleable proof-of-concept pipeline that lays the groundwork for analysis of multiple streams of semi-structured data posted on social media is demonstrated. Preliminary analysis and performance metrics are presented and discussed. Future work is described that will scale the system to cloud-based, real-time, analysis of multiple data streams, with Information Extraction (IE) (ex. sentiment analysis) and Machine Learning capability.
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Towards an Ontology-Driven Blockchain Design for Supply Chain Provenance

2016-01-01
Henry Kim , Marek Laskowski
An interesting research problem in our age of Big Data is that of determining provenance. Granular evaluation of provenance of physical goods -- e.g. tracking ingredients of a pharmaceutical or … An interesting research problem in our age of Big Data is that of determining provenance. Granular evaluation of provenance of physical goods -- e.g. tracking ingredients of a pharmaceutical or demonstrating authenticity of luxury goods -- has often not been possible with today's items that are produced and transported in complex, inter-organizational, often internationally-spanning supply chains. Recent adoption of Internet of Things and Blockchain technologies give promise at better supply chain provenance. We are particularly interested in the blockchain as many favoured use cases of blockchain are for provenance tracking. We are also interested in applying ontologies as there has been some work done on knowledge provenance, traceability, and food provenance using ontologies. In this paper, we make a case for why ontologies can contribute to blockchain design. To support this case, we analyze a traceability ontology and translate some of its representations to smart contracts that execute a provenance trace and enforce traceability constraints on the Ethereum blockchain platform.
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A conditional construction of Artin representations for real analytic Siegel cusp forms of weight (2,1)

2016-01-01
Henry Kim , Takuya Yamauchi

Rapid Prototyping of a Text Mining Application for Cryptocurrency Market Intelligence

2016-01-01
Marek Laskowski , Henry Kim
Blockchain represents a technology for establishing a shared, immutable version of the truth between a network of participants that do not trust one another, and therefore has the potential to … Blockchain represents a technology for establishing a shared, immutable version of the truth between a network of participants that do not trust one another, and therefore has the potential to disrupt any financial or other industries that rely on third-parties to establish trust. Recent trends in computing including: prevalence of Free and Open Source Software (FOSS); easy access to High Performance Computing (HPC i.e. 'The Cloud'); and increasingly advanced analytics capabilities such as Natural Language Processing (NLP) and Machine Learning (ML) allow for rapidly prototyping applications for analysis of trends in the emergence of Blockchain technology. A scaleable proof-of-concept pipeline that lays the groundwork for analysis of multiple streams of semi-structured data posted on social media is demonstrated. Preliminary analysis and performance metrics are presented and discussed. Future work is described that will scale the system to cloud-based, real-time, analysis of multiple data streams, with Information Extraction (IE) (ex. sentiment analysis) and Machine Learning capability.
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Data Analytics using Ontologies of Management Theories: Towards Implementing 'From Theory to Practice'

2016-01-01
Henry Kim , Jackie Ho Nam Cheung , Marek Laskowski +1 more
We explore how computational ontologies can be impactful vis-a-vis the developing discipline of "data science." We posit an approach wherein management theories are represented as formal axioms, and then applied … We explore how computational ontologies can be impactful vis-a-vis the developing discipline of "data science." We posit an approach wherein management theories are represented as formal axioms, and then applied to draw inferences about data that reside in corporate databases. That is, management theories would be implemented as rules within a data analytics engine. We demonstrate a case study development of such an ontology by formally representing an accounting theory in First-Order Logic. Though quite preliminary, the idea that an information technology, namely ontologies, can potentially actualize the academic cliche, "From Theory to Practice," and be applicable to the burgeoning domain of data analytics is novel and exciting.
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Towards an Ontology-Driven Blockchain Design for Supply Chain Provenance

2016-01-01
Henry Kim , Marek Laskowski
An interesting research problem in our age of Big Data is that of determining provenance. Granular evaluation of provenance of physical goods--e.g. tracking ingredients of a pharmaceutical or demonstrating authenticity … An interesting research problem in our age of Big Data is that of determining provenance. Granular evaluation of provenance of physical goods--e.g. tracking ingredients of a pharmaceutical or demonstrating authenticity of luxury goods--has often not been possible with today's items that are produced and transported in complex, inter-organizational, often internationally-spanning supply chains. Recent adoption of Internet of Things and Blockchain technologies give promise at better supply chain provenance. We are particularly interested in the blockchain as many favoured use cases of blockchain are for provenance tracking. We are also interested in applying ontologies as there has been some work done on knowledge provenance, traceability, and food provenance using ontologies. In this paper, we make a case for why ontologies can contribute to blockchain design. To support this case, we analyze a traceability ontology and translate some of its representations to smart contracts that execute a provenance trace and enforce traceability constraints on the Ethereum blockchain platform.
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Weakly holomorphic modular forms and rank two hyperbolic Kac-Moody algebras

2015-03-13
Henry Kim , Kyu‐Hwan Lee , Yichao Zhang
In this paper, we compute basis elements of certain spaces of weight <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="0"> <mml:semantics> <mml:mn>0</mml:mn> <mml:annotation encoding="application/x-tex">0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> weakly holomorphic modular forms and consider … In this paper, we compute basis elements of certain spaces of weight <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="0"> <mml:semantics> <mml:mn>0</mml:mn> <mml:annotation encoding="application/x-tex">0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> weakly holomorphic modular forms and consider the integrality of Fourier coefficients of the modular forms. We use the results to construct automorphic correction of the rank <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2"> <mml:semantics> <mml:mn>2</mml:mn> <mml:annotation encoding="application/x-tex">2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> hyperbolic Kac-Moody algebras <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper H left-parenthesis a right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">H</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>a</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathcal H(a)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="a equals 4 comma 5 comma 6"> <mml:semantics> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> <mml:mo>,</mml:mo> <mml:mn>5</mml:mn> <mml:mo>,</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">a=4,5,6</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, through Hilbert modular forms explicitly given by Borcherds lifts of the weakly holomorphic modular forms. We also compute asymptotics of the Fourier coefficients as they are related to root multiplicities of the rank <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2"> <mml:semantics> <mml:mn>2</mml:mn> <mml:annotation encoding="application/x-tex">2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> hyperbolic Kac-Moody algebras. This work is a continuation of an earlier work of the first and second authors, where automorphic correction was constructed for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper H left-parenthesis a right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">H</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>a</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathcal H(a)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="a equals 3 comma 11 comma 66"> <mml:semantics> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mn>11</mml:mn> <mml:mo>,</mml:mo> <mml:mn>66</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">a=3, 11, 66</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.
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Quantum affine algebras, canonical bases, and<i>q</i>-deformation of arithmetical functions

2012-04-10
Henry Kim , Kyu‐Hwan Lee
We obtain affine analogs of the Gindikin-Karpelevich and Casselman-Shalika formulas as sums over Kashiwara and Lusztig's canonical bases.As suggested by these formulas, we define natural q-deformation of arithmetical functions such … We obtain affine analogs of the Gindikin-Karpelevich and Casselman-Shalika formulas as sums over Kashiwara and Lusztig's canonical bases.As suggested by these formulas, we define natural q-deformation of arithmetical functions such as (multi)partition functions and Ramanujan τ -functions, and prove various identities among them.In some examples we recover classical identities by taking limits.Additionally, we consider q-deformation of the Kostant function and study certain q-polynomials whose special values are weight multiplicities.
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Data Analytics Using Ontologies of Management Theories: Towards Implementing 'From Theory to Practice'

2012-01-01
Henry Kim , Iryna Gel , Ho-Nam Cheung +1 more
Download This Paper Open PDF in Browser Add Paper to My Library Share: Permalink Using these links will ensure access to this page indefinitely Copy URL Copy DOI Download This Paper Open PDF in Browser Add Paper to My Library Share: Permalink Using these links will ensure access to this page indefinitely Copy URL Copy DOI
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Local 𝐿-functions and functional equations

2009-03-09
James Cogdell , Henry Kim , M. Narasimha Murty

Eulerian integral representations

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

The Kim-Sarnak theorem

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Generic representations and their Whittaker models

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Local 𝐿-functions: The non-Archimedean case

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

The Langlands-Tunnell theorem

2009-03-09
James Cogdell , Henry Kim , M. Narasimha Murty

Eisenstein series and constant terms

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Modular forms and their 𝐿-functions

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

𝐿-groups and automorphic 𝐿-functions

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Oscillations of Fourier coefficients of cusp forms

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Functoriality of the symmetric fourth

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Zeros and poles of Artin 𝐿-functions

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Introduction to Artin 𝐿-functions

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty

Langlands functoriality conjecture

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty
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Holomorphy and bounded in vertical strips

2009-03-09
James Cogdell , Henry Kim , M. Narasimha Murty
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Functoriality of the symmetric cube

2009-03-09
James Cogdell , Henry Kim , M. Murty

Local Langlands correspondence

2009-03-09
James Cogdell , Henry Kim , M. Narasimha Murty
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Meromorphic continuation of 𝐿-functions

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty
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Kloosterman sums and Selberg’s conjecture

2009-03-09
James Cogdell , Henry Kim , M. Ram Murty
Coauthor Papers Together
James Cogdell 29
M. Ram Murty 20
Marek Laskowski 17
Hjalmar Turesson 8
M. Narasimha Murty 6
Shivam Saxena 5
Hany E. Z. Farag 5
Iryna Gel 3
Aidan Brookson 3
Kyu‐Hwan Lee 2
Jöerg Evermann 2
Jackie Ho Nam Cheung 2
M. Murty 2
Ning Nan 2
Alexandra Roatiş 2
M. Murty 1
Herbert D. Aronow 1
Percival Lucena 1
Khaldoon Alaswad 1
Brittany Fuller 1
Yichao Zhang 1
Takuya Yamauchi 1
Ho-Nam Cheung 1
Pedro Villablanca 1
Vikas Aggarwal 1
Danil Kabanov 1
Asaad Nakhle 1
Ahmad Jabri 1
Alécio Pedro Delazari Binotto 1
Peter J. Cho 1
Brian O’Neill 1
Pedro Engel Gonzalez 1
Mir B. Basir 1
William O’Neill 1
Gerald Koenig 1
Mohammad Alqarqaz 1
Hidenori Katsurada 1
Benjamin C. Hofeld 1
Muhammad Memon 1
Raef Fadel 1
Tiberio Frisoli 1
Fernanda da Silva Momo 1
Matt Barlin 1
Michael Zargham 1

Towards an Ontology-Driven Blockchain Design for Supply Chain Provenance

2016-01-01
Henry Kim , Marek Laskowski
An interesting research problem in our age of Big Data is that of determining provenance. Granular evaluation of provenance of physical goods -- e.g. tracking ingredients of a pharmaceutical or … An interesting research problem in our age of Big Data is that of determining provenance. Granular evaluation of provenance of physical goods -- e.g. tracking ingredients of a pharmaceutical or demonstrating authenticity of luxury goods -- has often not been possible with today's items that are produced and transported in complex, inter-organizational, often internationally-spanning supply chains. Recent adoption of Internet of Things and Blockchain technologies give promise at better supply chain provenance. We are particularly interested in the blockchain as many favoured use cases of blockchain are for provenance tracking. We are also interested in applying ontologies as there has been some work done on knowledge provenance, traceability, and food provenance using ontologies. In this paper, we make a case for why ontologies can contribute to blockchain design. To support this case, we analyze a traceability ontology and translate some of its representations to smart contracts that execute a provenance trace and enforce traceability constraints on the Ethereum blockchain platform.
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Influenza H3N2 variant viruses with pandemic potential: Preventing catastrophe in remote and isolated Canadian communities

2013-04-28
Marek Laskowski , Venkata R. Duvvuri , David L. Buckeridge +3 more

Agent-Based Modeling of the Spread of Influenza-Like Illness in an Emergency Department: A Simulation Study

2011-08-03
M. Laskowski , Bryan Demianyk , Julia Witt +3 more
The objective of this paper was to develop an agent-based modeling framework in order to simulate the spread of influenza virus infection on a layout based on a representative hospital … The objective of this paper was to develop an agent-based modeling framework in order to simulate the spread of influenza virus infection on a layout based on a representative hospital emergency department in Winnipeg, Canada. In doing so, the study complements mathematical modeling techniques for disease spread, as well as modeling applications focused on the spread of antibiotic-resistant nosocomial infections in hospitals. Twenty different emergency department scenarios were simulated, with further simulation of four infection control strategies. The agent-based modeling approach represents systems modeling, in which the emergency department was modeled as a collection of agents (patients and healthcare workers) and their individual characteristics, behaviors, and interactions. The framework was coded in C++ using Qt4 libraries running under the Linux operating system. A simple ordinary least squares (OLS) regression was used to analyze the data, in which the percentage of patients that became infected in one day within the simulation was the dependent variable. The results suggest that within the given instance context, patient-oriented infection control policies (alternate treatment streams, masking symptomatic patients) tend to have a larger effect than policies that target healthcare workers. The agent-based modeling framework is a flexible tool that can be made to reflect any given environment; it is also a decision support tool for practitioners and policymakers to assess the relative impact of infection control strategies. The framework illuminates scenarios worthy of further investigation, as well as counterintuitive findings.

Toward Standardizing a Lexicon of Infectious Disease Modeling Terms

2016-09-27
Rachael M. Milwid , Andreea Steriu , Julien Arino +7 more
Disease modeling is increasingly being used to evaluate the effect of health intervention strategies, particularly for infectious diseases. However, the utility and application of such models are hampered by the … Disease modeling is increasingly being used to evaluate the effect of health intervention strategies, particularly for infectious diseases. However, the utility and application of such models are hampered by the inconsistent use of infectious disease modeling terms between and within disciplines. We sought to standardize the lexicon of infectious disease modeling terms and develop a glossary of terms commonly used in describing models' assumptions, parameters, variables, and outcomes. We combined a comprehensive literature review of relevant terms with an online forum discussion in a virtual community of practice, mod4PH (Modeling for Public Health). Using a convergent discussion process and consensus amongst the members of mod4PH, a glossary of terms was developed as an online resource. We anticipate that the glossary will improve inter- and intradisciplinary communication and will result in a greater uptake and understanding of disease modeling outcomes in heath policy decision-making. We highlight the role of the mod4PH community of practice and the methodologies used in this endeavor to link theory, policy, and practice in the public health domain.
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Infinite-Dimensional Lie Algebras

1990-09-20
Victor G. Kač
This is the third, substantially revised edition of this important monograph. The book is concerned with Kac–Moody algebras, a particular class of infinite-dimensional Lie algebras, and their representations. It is … This is the third, substantially revised edition of this important monograph. The book is concerned with Kac–Moody algebras, a particular class of infinite-dimensional Lie algebras, and their representations. It is based on courses given over a number of years at MIT and in Paris, and is sufficiently self-contained and detailed to be used for graduate courses. Each chapter begins with a motivating discussion and ends with a collection of exercises, with hints to the more challenging problems.
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Blockchains for Business Process Management - Challenges and Opportunities

2018-02-26
Jan Mendling , Ingo Weber , Wil M. P. van der Aalst +7 more
Blockchain technology offers a sizable promise to rethink the way interorganizational business processes are managed because of its potential to realize execution without a central party serving as a single … Blockchain technology offers a sizable promise to rethink the way interorganizational business processes are managed because of its potential to realize execution without a central party serving as a single point of trust (and failure). To stimulate research on this promise and the limits thereof, in this article, we outline the challenges and opportunities of blockchain for business process management (BPM). We first reflect how blockchains could be used in the context of the established BPM lifecycle and second how they might become relevant beyond. We conclude our discourse with a summary of seven research directions for investigating the application of blockchain technology in the context of BPM.
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Representations of GL(n) and division algebras over a p-adic field

1983-03-01
Jonathan David Rogawski

The digital traces of bubbles: feedback cycles between socio-economic signals in the Bitcoin economy

2014-08-06
David García , Claudio J. Tessone , Pavlin Mavrodiev +1 more
What is the role of social interactions in the creation of price bubbles? Answering this question requires obtaining collective behavioural traces generated by the activity of a large number of … What is the role of social interactions in the creation of price bubbles? Answering this question requires obtaining collective behavioural traces generated by the activity of a large number of actors. Digital currencies offer a unique possibility to measure socio-economic signals from such digital traces. Here, we focus on Bitcoin, the most popular cryptocurrency. Bitcoin has experienced periods of rapid increase in exchange rates (price) followed by sharp decline; we hypothesize that these fluctuations are largely driven by the interplay between different social phenomena. We thus quantify four socio-economic signals about Bitcoin from large datasets: price on online exchanges, volume of word-of-mouth communication in online social media, volume of information search and user base growth. By using vector autoregression, we identify two positive feedback loops that lead to price bubbles in the absence of exogenous stimuli: one driven by word of mouth, and the other by new Bitcoin adopters. We also observe that spikes in information search, presumably linked to external events, precede drastic price declines. Understanding the interplay between the socio-economic signals we measured can lead to applications beyond cryptocurrencies to other phenomena that leave digital footprints, such as online social network usage.
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The Impact of Demographic Variables on Disease Spread: Influenza in Remote Communities

2011-10-04
Marek Laskowski , Luiz C. Mostaço-Guidolin , Amy L. Greer +2 more
The role of demographic variables in disease spread in remote and isolated communities is poorly understood. We developed an agent-based model of a small indigenous community to qualitatively study the … The role of demographic variables in disease spread in remote and isolated communities is poorly understood. We developed an agent-based model of a small indigenous community to qualitatively study the impact of pre-existing immunity in both young and elderly populations. We observed that in crowded living conditions, the age distribution of the population is a critical factor influencing epidemic spread. As the average age of the population increases, the effect of the pre-existing immunity in older individuals becomes more pronounced in decreasing disease incidence, even when pre-existing immunity levels in young individuals are low. However, in a non-crowded setting with relatively low average persons-per-household, the pre-existing immunity levels of young individuals remains a determining factor, regardless of the age distribution of the population. We suggest that for optimizing public health policies, social and demographic complexities of the remote and vulnerable communities should be carefully evaluated in modeling intervention strategies.
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Optimized Execution of Business Processes on Blockchain

2017-01-01
Luciano García‐Bañuelos , Alexander Ponomarev , Marlon Dumas +1 more
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The local Langlands conjecture for GL ( n ) over a p -adic field, n &lt; p

1998-09-17
Michael Harris

Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique

2000-02-01
Guy Henniart

Nowcasting the Bitcoin Market with Twitter Signals

2014-06-30
Jermain Kaminski , Peter A. Gloor
This paper analyzes correlations and causalities between Bitcoin market indicators and Twitter posts containing emotional signals on Bitcoin. Within a timeframe of 104 days (November 23rd 2013 - March 7th … This paper analyzes correlations and causalities between Bitcoin market indicators and Twitter posts containing emotional signals on Bitcoin. Within a timeframe of 104 days (November 23rd 2013 - March 7th 2014), about 160,000 Twitter posts containing bitcoin and a positive, negative or uncertainty related term were collected and further analyzed. For instance, the terms happy, love, fun, good, bad, sad and unhappy represent positive and negative emotional signals, while hope, fear and worry are considered as indicators of uncertainty. The static (daily) Pearson correlation results show a significant positive correlation between emotional tweets and the close price, trading volume and intraday price spread of Bitcoin. However, a dynamic Granger causality analysis does not confirm a statistically significant effect of emotional Tweets on Bitcoin market values. To the contrary, the analyzed data shows that a higher Bitcoin trading volume Granger causes more signals of uncertainty within a 24 to 72-hour timeframe. This result leads to the interpretation that emotional sentiments rather mirror the market than that they make it predictable. Finally, the conclusion of this paper is that the microblogging platform Twitter is Bitcoin's virtual trading floor, emotionally reflecting its trading dynamics.

Information flow in social groups

2004-02-11
Fang Wu , Bernardo A. Huberman , Lada A. Adamic +1 more
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Artin’s conjecture for representations of octahedral type

1981-01-01
Jerrold B. Tunnell
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A contribution to the mathematical theory of epidemics

1927-08-01
W. O. Kermack , A. G. McKendrick
(1) One of the most striking features in the study of epidemics is the difficulty of finding a causal factor which appears to be adequate to account for the magnitude … (1) One of the most striking features in the study of epidemics is the difficulty of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population. It was with a view to obtaining more insight regarding the effects of the various factors which govern the spread of contagious epidemics that the present investigation was undertaken. Reference may here be made to the work of Ross and Hudson (1915-17) in which the same problem is attacked. The problem is here carried to a further stage, and it is considered from a point of view which is in one sense more general. The problem may be summarised as follows: One (or more) infected person is introduced into a community of individuals, more or less susceptible to the disease in question. The disease spreads from the affected to the unaffected by contact infection. Each infected person runs through the course of his sickness, and finally is removed from the number of those who are sick, by recovery or by death. The chances of recovery or death vary from day to day during the course of his illness. The chances that the affected may convey infection to the unaffected are likewise dependent upon the stage of the sickness. As the epidemic spreads, the number of unaffected members of the community becomes reduced. Since the course of an epidemic is short compared with the life of an individual, the population may be considered as remaining constant, except in as far as it is modified by deaths due to the epidemic disease itself. In the course of time the epidemic may come to an end. One of the most important probems in epidemiology is to ascertain whether this termination occurs only when no susceptible individuals are left, or whether the interplay of the various factors of infectivity, recovery and mortality, may result in termination, whilst many susceptible individuals are still present in the unaffected population. It is difficult to treat this problem in its most general aspect. In the present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.

ModelChain: Decentralized Privacy-Preserving Healthcare Predictive Modeling Framework on Private Blockchain Networks

2018-01-01
Tsung-Ting Kuo , Lucila Ohno‐Machado
Cross-institutional healthcare predictive modeling can accelerate research and facilitate quality improvement initiatives, and thus is important for national healthcare delivery priorities. For example, a model that predicts risk of re-admission … Cross-institutional healthcare predictive modeling can accelerate research and facilitate quality improvement initiatives, and thus is important for national healthcare delivery priorities. For example, a model that predicts risk of re-admission for a particular set of patients will be more generalizable if developed with data from multiple institutions. While privacy-protecting methods to build predictive models exist, most are based on a centralized architecture, which presents security and robustness vulnerabilities such as single-point-of-failure (and single-point-of-breach) and accidental or malicious modification of records. In this article, we describe a new framework, ModelChain, to adapt Blockchain technology for privacy-preserving machine learning. Each participating site contributes to model parameter estimation without revealing any patient health information (i.e., only model data, no observation-level data, are exchanged across institutions). We integrate privacy-preserving online machine learning with a private Blockchain network, apply transaction metadata to disseminate partial models, and design a new proof-of-information algorithm to determine the order of the online learning process. We also discuss the benefits and potential issues of applying Blockchain technology to solve the privacy-preserving healthcare predictive modeling task and to increase interoperability between institutions, to support the Nationwide Interoperability Roadmap and national healthcare delivery priorities such as Patient-Centered Outcomes Research (PCOR).

Transforming Energy Networks via Peer-to-Peer Energy Trading: The Potential of Game-Theoretic Approaches

2018-06-27
Wayes Tushar , Chau Yuen , Hamed Mohsenian‐Rad +3 more
Peer-to-peer (P2P) energy trading has emerged as a next-generation energy-management mechanism for the smart grid that enables each prosumer (i.e., an energy consumer who also produces electricity) of the network … Peer-to-peer (P2P) energy trading has emerged as a next-generation energy-management mechanism for the smart grid that enables each prosumer (i.e., an energy consumer who also produces electricity) of the network to participate in energy trading with other prosumers and the grid. This poses a significant challenge in terms of modeling the decisionmaking process of the participants' conflicting interests and motivating prosumers to participate in energy trading and cooperate, if necessary, in achieving different energy-management goals. Therefore, such a decisionmaking process needs to be built on solid mathematical and signal processing principles that can ensure an efficient operation of the electric power grid. This article provides an overview of the use of game-theoretic approaches for P2P energy trading as a feasible and effective means of energy management. Various game- and auction-theoretic approaches are discussed by following a systematic classification to provide information on the importance of game theory for smart energy research. This article also focuses on the key features of P2P energy trading and gives an introduction to an existing P2P testbed. Furthermore, the article gives specific game- and auction-theoretic models that have recently been used in P2P energy trading and discusses important findings arising from these approaches.
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On 𝑝-adic Hermitian Eisenstein series

2006-03-23
Shōyū Nagaoka
In this paper we generalize the notion of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic modular form to the Hermitian modular case and prove a … In this paper we generalize the notion of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic modular form to the Hermitian modular case and prove a formula that shows a coincidence between certain <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic Hermitian Eisenstein series and the genus theta series associated with Hermitian matrix with determinant <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.

Prioritizing Consumers in Smart Grid: A Game Theoretic Approach

2014-04-11
Wayes Tushar , J. Andrew Zhang , David B. Smith +2 more
This paper proposes an energy management technique for a consumer-to-grid system in smart grid. The benefit to consumers is made the primary concern to encourage consumers to participate voluntarily in … This paper proposes an energy management technique for a consumer-to-grid system in smart grid. The benefit to consumers is made the primary concern to encourage consumers to participate voluntarily in energy trading with the central power station (CPS) in situations of energy deficiency. A novel system model motivating energy trading under the goal of social optimality is proposed. A single-leader multiple-follower Stackelberg game is then studied to model the interactions between the CPS and a number of energy consumers (ECs), and to find optimal distributed solutions for the optimization problem based on the system model. The CPS is considered as a leader seeking to minimize its total cost of buying energy from the ECs, and the ECs are the followers who decide on how much energy they will sell to the CPS for maximizing their utilities. It is shown that the game, which can be implemented distributedly, possesses a socially optimal solution, in which the sum of the benefits to all consumers is maximized, as the total cost to the CPS is minimized. Numerical analysis confirms the effectiveness of the game.
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Introduction to Quantum Groups

2010-01-01
G. Lusztig
According to Drinfeld, a quantum group is the same as a Hopf algebra. This includes as special cases, the algebra of regular functions on an algebraic group and the enveloping … According to Drinfeld, a quantum group is the same as a Hopf algebra. This includes as special cases, the algebra of regular functions on an algebraic group and the enveloping algebra of a semisimple

A character-sum estimate and applications

1998-01-01
Karl K. Norton
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Kloosterman sums and Fourier coefficients of cusp forms

1982-06-01
Jean‐Marc Deshouillers , Henryk Iwaniec

On some p-adic properties of Siegel–Eisenstein series

2003-09-12
Hidenori Katsurada , Shōyū Nagaoka

Fourier Transforms of Intertwining Operators and Plancherel Measures for GL(n)

1984-02-01
Freydoon Shahidi

On the λ-adic representations associated to some simple Shimura varieties

1992-12-01
Robert Kottwitz

On the Functional Equations Satisfied by Eisenstein Series

1976-01-01
R. P. Langlands
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Note onp-adic Hermitian Eisenstein Series

2006-12-01
T. Munemoto , Shōyū Nagaoka

Intertwining operators and composition series of generalized and degenerate principal series for Sp(4,R)

2009-12-08
Goran Muić
In this paper we study analytic properties of intertwining operators and apply them to the determination of the composition series of degenerate and generalized principal series for Sp(4, R).We expect … In this paper we study analytic properties of intertwining operators and apply them to the determination of the composition series of degenerate and generalized principal series for Sp(4, R).We expect that that some of the methods developed here will extend to higher rank groups in order to extend the formalism of degenerate Eisenstein series given by [21] and [22].In higher rank cases we expect to be more dependent on the algebraic theory of representation theory of the real reductive groups as developed by Vogan [30].
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Signature quantization and representations of compact Lie groups

2004-07-07
Victor Guillemin , Etienne Rassart
We discuss some applications of signature quantization to the representation theory of compact Lie groups. In particular, we prove signature analogues of the Kostant formula for weight multiplicities and the … We discuss some applications of signature quantization to the representation theory of compact Lie groups. In particular, we prove signature analogues of the Kostant formula for weight multiplicities and the Steinberg formula for tensor product multiplicities. Using symmetric functions, we also find, for type A , analogues of the Weyl branching rule and the Gel'fand–Tsetlin theorem.
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Applications of Langlands’ functorial lift of odd orthogonal groups

2002-03-06
Henry H. Kim
Together with Cogdell, Piatetski-Shapiro and Shahidi, we proved earlier the existence of a weak functorial lift of a generic cuspidal representation of $SO_{2n+1}$ to $GL_{2n}$. Recently, Ginzburg, Rallis and Soudry … Together with Cogdell, Piatetski-Shapiro and Shahidi, we proved earlier the existence of a weak functorial lift of a generic cuspidal representation of $SO_{2n+1}$ to $GL_{2n}$. Recently, Ginzburg, Rallis and Soudry obtained a more precise form of the lift using their integral representation technique, namely, the lift is an isobaric sum of cuspidal representations of $GL_{n_i}$ (more precisely, cuspidal representations of $GL_{2n_i}$ such that the exterior square $L$-functions have a pole at $s=1$). One purpose of this paper is to give a simpler proof of this fact in the case that a cuspidal representation has one supercuspidal component. In a separate paper, we prove it without any condition using a result on spherical unitary dual due to Barbasch and Moy. We give several applications of the functorial lift: First, we parametrize square integrable representations with generic supercuspidal support, which have been classified by Moeglin and Tadic. Second, we give a criterion for cuspidal reducibility of supercuspidal representations of $GL_m\times SO_{2n+1}$. Third, we obtain a functorial lift from generic cuspidal representations of $SO_5$ to automorphic representations of $GL_5$, corresponding to the $L$-group homomorphism $Sp_4(\mathbb {C})\longrightarrow GL_5(\mathbb {C})$, given by the second fundamental weight.
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Exceptional modular form of weight 4 on an exceptional domain contained in $\mathbb C^27$

1993-04-30
Henry H. Kim
Resnikoff [12] proved that weights of a non trivial singular modular form should be integral multiples of 1/2, 1, 2, 4 for the Siegel, Hermitian, quaternion and exceptional cases, respectively. … Resnikoff [12] proved that weights of a non trivial singular modular form should be integral multiples of 1/2, 1, 2, 4 for the Siegel, Hermitian, quaternion and exceptional cases, respectively. The \theta -functions in the Siegel, Hermitian and quaternion cases provide examples of singular modular forms (Krieg [10]). Shimura [15] obtained a modular form of half-integral weight by analytically continuing an Eisenstein series. Bump and Baily suggested the possibility of applying an analogue of Shimura's method to obtain singular modular forms, i. e. modular forms of weight 4 and 8, on the exceptional domain of 3 x 3 hermitian matrices over Cayley numbers. The idea is to use Fourier expansion of a non-holomorphic Eisenstein series defined by using the factor of automorphy as in Karel [7]. The Fourier coefficients are the product of confluent hypergeometric functions as in Nagaoka [11] and certain singular series which we calculate by the method of Karel [6]. In this note we describe a modular form of weight 4 which may be viewed as an analogue of a \theta zero-value and as an application, we consider its Mellin transform and prove a functional equation of the Eisenstein series which is a Nagaoka's conjecture (Nagaoka [11]).
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The singular modular forms on the 27-dimensional exceptional domain

1997-12-01
Aloys Krieg

A hyperbolic Kac-Moody algebra and the theory of Siegel modular forms of genus 2

1983-03-01
Alex J. Feingold , Igor Frenkel

Crystal bases and two-sided cells of quantum affine algebras

2004-06-01
Jonathan Beck , Hiraku Nakajima
Let $\mathfrak{g}$ be an affine Kac-Moody Lie algebra. Let $\mathbf{U}^+$ be the positive part of the Drinfeld-Jimbo quantum enveloping algebra associated to $\mathfrak{g}$. We construct a basis of $\mathbf{U}^+$ which … Let $\mathfrak{g}$ be an affine Kac-Moody Lie algebra. Let $\mathbf{U}^+$ be the positive part of the Drinfeld-Jimbo quantum enveloping algebra associated to $\mathfrak{g}$. We construct a basis of $\mathbf{U}^+$ which is related to the Kashiwara-Lusztig global crystal basis (or canonical basis) by an upper-triangular matrix (with respect to an explicitly defined ordering) with 1's on the diagonal and with above-diagonal entries in $q_s^{-1} \mathbf{Z}[q_s^{-1}]$. Using this construction, we study the global crystal basis $\mathscr{B}(\widetilde{\mathbf{U}})$ of the modified quantum enveloping algebra defined by Lusztig. We obtain a Peter-Weyl-like decomposition of the crystal $\mathscr{B}(\widetilde{\mathbf{U}})$ (Th. 4.18), as well as an explicit description of two-sided cells of $\mathscr{B}(\widetilde{\mathbf{U}})$ and the limit algebra of $\widetilde{\mathbf{U}}$ at $q=0$ (Th. 6.44).

On Euler Products and the Classification of Automorphic Representations I

1981-06-01
H. Jacquet , J. A. Shalika

The trace formula and Drinfeld’s upper halfplane

1994-11-01
Герд Фалтингс

On the Saito-Kurokawa lifting

1983-06-01
Ilya Piatetski-Shapiro

Generic transfer for general spin groups

2006-03-01
Mahdi Asgari , Freydoon Shahidi
We prove Langlands functoriality for the generic spectrum of general spin groups (both odd and even). Contrary to other recent instances of functoriality, our resulting automorphic representations on the general … We prove Langlands functoriality for the generic spectrum of general spin groups (both odd and even). Contrary to other recent instances of functoriality, our resulting automorphic representations on the general linear group are not self-dual. Together with cases of classical groups, this completes the list of cases of split reductive groups whose L-groups have classical derived groups. The important transfer from GSp4 to GL4 follows from our result as a special case
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Boundedness of automorphic 𝐿–functions in vertical strips

2000-09-18
Stephen Gelbart , Freydoon Shahidi
In this paper we prove the boundedness in vertical strips of finite width for all the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding="application/x-tex">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>–functions that … In this paper we prove the boundedness in vertical strips of finite width for all the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding="application/x-tex">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>–functions that appear in constant terms of Eisenstein series, under a certain natural assumption on local normalized intertwining operators. This result has been quite important in establishing recent cases of Langlands functoriality by Cogdell, Kim, Piatetski-Shapiro, and Shahidi, using converse theorems.

Functorial Products for GL 2 × GL 3 and the Symmetric Cube for GL 2

2002-05-01
Henry H. Kim , Freydoon Shahidi
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Companion forms in parallel weight one

2013-05-10
Toby Gee , Payman L Kassaei
Abstract Let $p\gt 2$ be prime, and let $F$ be a totally real field in which $p$ is unramified. We give a sufficient criterion for a $\mathrm{mod} \hspace{0.167em} p$ Galois … Abstract Let $p\gt 2$ be prime, and let $F$ be a totally real field in which $p$ is unramified. We give a sufficient criterion for a $\mathrm{mod} \hspace{0.167em} p$ Galois representation to arise from a $\mathrm{mod} \hspace{0.167em} p$ Hilbert modular form of parallel weight one, by proving a ‘companion forms’ theorem in this case. The techniques used are a mixture of modularity lifting theorems and geometric methods. As an application, we show that Serre’s conjecture for $F$ implies Artin’s conjecture for totally odd two-dimensional representations over $F$ .
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EULER PRODUCTS FOR CONGRUENCE SUBGROUPS OF THE SIEGEL GROUP OF GENUS 2

1976-04-30
С. А. Евдокимов
In this paper the construction is begun of a theory of Dirichlet series with Euler expansion which correspond to analytic automorphic forms for congruence subgroups of the integral symplectic group … In this paper the construction is begun of a theory of Dirichlet series with Euler expansion which correspond to analytic automorphic forms for congruence subgroups of the integral symplectic group of genus 2. Namely, for an arbitrary positive integer a connection is revealed between the eigenvalues of an eigenfunction of all the Hecke operators , where is the principal congruence subgroup of degree of the group , and its Fourier coefficients. This connection can be written in the language of Dirichlet series in the form of identities; here an infinite sequence of identities arises, indexed by classes of positive definite integral primitive binary quadratic forms equivalent modulo the principal congruence subgroup of degree of . Bibliography: 15 titles.

Analytic Proof of the Strong Multiplicity One Theorem

1985-02-01
Carlos Moreno

An isomorphism between scalar-valued modular forms and modular forms for Weil representations

2014-07-17
Yichao Zhang
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Hyperbolic Lie algebras and quasi-regular cusps on Hilbert modular surfaces

1979-02-01
James Lepowsky , Robert V. Moody

Igusa modular forms and 'the simplest' Lorentzian Kac-Moody algebras

1996-12-31
Valery Gritsenko , Vadim V. Nikulin
We find automorphic corrections for the Lorentzian Kac--Moody algebras with the simplest generalized Cartan matrices of rank 3: A_{1,0} = 2 0 -1 0 2 -2 -1 -2 2 and … We find automorphic corrections for the Lorentzian Kac--Moody algebras with the simplest generalized Cartan matrices of rank 3: A_{1,0} = 2 0 -1 0 2 -2 -1 -2 2 and A_{1,I} = 2 -2 -1 -2 2 -1 -1 -1 2 For A_{1,0} this correction is given by the Igusa Sp_4(Z)-modular form \chi_{35} of weight 35, and for A_{1,I} by a Siege modular form of weight 30 with respect to a 2-congruence subgroup. We find infinite product or sum expansions for these forms. Our method of construction of \chi_{35} leads to the direct construction of Siegel modular forms by infinite product expansions, whose divisors are the Humbert surfaces with fixed discriminants. Existence of these forms was proved by van der Geer in 1982 using some geometrical consideration. We announce a list of all hyperbolic symmetric generalized Cartan matrices A of rank 3 such that A has elliptic or parabolic type, A has a lattice Weyl vector, and A contains the affine submatrix \tilde{A}_1.
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On ArtinL-functions associated to Hilbert modular forms of weight one

1983-02-01
Jonathan David Rogawski , Jerrold B. Tunnell

Cuspidality of symmetric powers with applications

2002-03-15
Henry H. Kim , Freydoon Shahidi
The purpose of this paper is to prove that the symmetric fourth power of a cusp form on ${\rm GL}(2)$, whose existence was proved earlier by the first author, is … The purpose of this paper is to prove that the symmetric fourth power of a cusp form on ${\rm GL}(2)$, whose existence was proved earlier by the first author, is cuspidal unless the corresponding automorphic representation is of dihedral, tetrahedral, or octahedral type. As a consequence, we prove a number of results toward the Ramanujan-Petersson and Sato-Tate conjectures. In particular, we establish the bound $q\sp {1/9}\sb v$ for unramified Hecke eigenvalues of cusp forms on ${\rm GL}(2)$. Over an arbitrary number field, this is the best bound available at present.

Explicit Determination of the Images of the Galois Representations Attached to Abelian Surfaces with End(A) = Z

2002-01-01
Luis Dieulefait
Abstract We give an effective version of a resuIt reported by Serre asserting that the images of the Galois representations attached to an abelian surface with End(A) = Z are … Abstract We give an effective version of a resuIt reported by Serre asserting that the images of the Galois representations attached to an abelian surface with End(A) = Z are as large as possible for almost every prime. Our algorithm depends on the truth of Serre's conjecture for two-dimensional odd irreducible Galois representations. Assuming this conjecture, we determine the finite set of primes with exceptional image. We also give infinite sets of primes for which we can prove (unconditionally) that the images of the corresponding Galois representations are large. We apply the results to a few examples of abelian surfaces. Keywords: Galois representationsabelian varieties
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